We will never know. But being optimistic and assuming it costs $349 to manufacture, and considering they bundled 2 games with it, and retailers also offered another full price free game with it also on black friday, retailers were technically selling each X1 for $229. But that's assuming MS pay Ubisoft $60 for each X1 AC Unity bundle sold. 

If you break down the $60 price, you would know that not all of the pie goes to the publishers. Especially, when the games are digital.

Ok, but how much do think goes to publishers in this situation? $20? $40? 

MS can afford it so its not really  that big of a deal right now.  This is all being done for show. If they were to keep it up it would become a problem. They'll go back to $400 in overall price and if Sony continues to wreck them they'll drop the price again between June-september. Its obvious that this isnt about profit because the Xbox One had been selling very well. Its just that when Sony sells well its on another level. MS had to devalue their console in the first year just to catch up to what Sony naturally sells at $400.

MS can easily afford it but with a new CEO in charge, and one who thinks "Xbox is not a core part of Microsoft", he might not be willing to keep a division which barely makes money. 

Also, each division within the company has its own budget and projections for the year.  So just because the parent company can afford it, it doesn't mean the XBox division can just spend whatever they want.   That's true for any big company, institutions, schools, etc.  

Exactly, hence why I said it cannot go on forever. Getting peoples attention will eventually become secondary to profitability. Eventually the wrecklessness has to stop for that particular department.

Playstation division lost these 1.2$b?

Has the XBOX brand ever made Microsoft any money? By this I mean total profit since the XBOX.

Honestly, I don't even know why Microsoft still bothers with XBOX. I guess they sort of have to continue now because of the big early investments during the original XBOX days. But still, Microsoft can't be happy overall with the XBOX brand.

And besides, since when does XBOX sell more games than PS? All games I see on VGCHARTZ sell A LOT more on PS4. And it's pretty easy to outperform Wii U lol. 

We don't have exact figures because Xbox is in the hardware division which has contained flops like Zune and stuff and losses can be covered up from Android royalties (which are huge for MS). But if I remember correctly, 360 overall was profitable. So it was able to recover the billions it lost in its first years on the market. However, the first Xbox lost over $4bn. So the division has most likely not recovered those gigantic losses. 

Here's something I found, although I'm not sure how accurate it is.